One of Nelson Mandela's daughters says the former South African president is "doing very well", as he spends a 10th day in a Pretoria hospital receiving treatment for a lung infection.

Mr Mandela, the nation's first black president, has been in a Pretoria hospital for more than a week undergoing treatment for a recurrent lung infection.

The government says Mr Mandela remains in a "serious but stable" condition, but Mr Mandela's daughter Zenani Mandela Dlamini has given a positive outlook after visiting the 94-year-old in hospital.

She told reporters outside the hospital: "He's doing very well".

Ms Mandela-Dlamini, who is South Africa's ambassador to Argentina, also joined other members of the family as they inspected the flowers and messages at the gates of the hospital where Mr Mandela is staying.

She is the eldest daughter from Mandela's marriage to his ex-wife Winnie.

His current wife, Graca Machel, has thanked members of the public for supporting the ailing anti-apartheid icon, saying they have eased "the burden of anxiety".

She says thousands of messages of support have arrived by phone, letter, email and social media.

School children have also gathered outside the Johannesburg home of the former president to sing hymns.

Ms Machel says she is grateful for the love and generosity the family has received from across South Africa and around the world.

"So much love and generosity ... has come our way to lighten the burden of anxiety; bringing us love, comfort and hope," she said in a statement.

"We have felt the closeness of the world and the deepest meaning of strength and peace.

"Our gratitude is difficult to express. But the love and peace we feel give yet more life to the simple 'thank you'."

Like many others, she has praise for what Mr Mandela stands for, but also anger and resentment at the ruling party he once led.

"I'm staying here from 2002, even now from this age, I don't have a house," she said.

In South Africa, white households are still at least six times richer than their black neighbours, according to the latest census.

Lerato Molio from the South African Institute for Race Relations says anger at the widening inequality is cause for concern.

"I think moving on we need to concentrate on our economic issues and the underlying reasons for why there are race tensions in the country to begin with," he said.

"When people are fighting for houses, when people are fighting for jobs, when people are fighting for a secure income, what happens is that differences are highlighted.

"And in the case of in townships where people that live in townships are black, you can't use race as sort of that drawing line, so something else needs to be used, and if it's not gender, it's going to be nationality."